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A Generalized Distance Function and the Analysis of Production Efficiency

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  • JEAN-PAUL CHAVAS

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  • THOMAS L. COX

Abstract

A generalization of Shephard’s distance functions is proposed, extending the usefulness of distance functions in economic analysis. Applications to efficiency measurements and productivity analysis are presented. New indexes of productivity and technical, allocative, and scale efficiency are proposed and analyzed. Interpretation of these indexes in terms of ray-average cost, ray-average revenue, and cost-to-revenue ratio is discussed.

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Bibliographic Info

Paper provided by Wisconsin-Madison Agricultural and Applied Economics Department in its series Wisconsin-Madison Agricultural and Applied Economics Staff Papers with number 422.

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Length: 43 pages
Date of creation: Feb 1999
Date of revision:
Handle: RePEc:wop:wisaes:422

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  1. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
  2. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
  3. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
  4. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  5. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
  6. Bauer, Paul W., 1990. "Recent developments in the econometric estimation of frontiers," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 39-56.
  7. Forsund, Finn R. & Lovell, C. A. Knox & Schmidt, Peter, 1980. "A survey of frontier production functions and of their relationship to efficiency measurement," Journal of Econometrics, Elsevier, vol. 13(1), pages 5-25, May.
  8. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
  9. Fare, Rolf & Shawna Grosskopf & Mary Norris & Zhongyang Zhang, 1994. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries," American Economic Review, American Economic Association, vol. 84(1), pages 66-83, March.
  10. Ray, Subhash C & Desli, Evangelia, 1997. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Comment," American Economic Review, American Economic Association, vol. 87(5), pages 1033-39, December.
  11. Lau, Lawrence J, 1972. "Profit Functions of Technologies with Multiple Inputs and Outputs," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 281-89, August.
  12. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
  13. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-32, November.
  14. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
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Cited by:
  1. Gelaw, Fekadu, 2013. "Inefficiency and Incapability Gaps as Causes of Poverty: A Poverty Line-Augmented Efficiency Analysis Using Stochastic Distance Function," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 8(2), August.
  2. Zofío, José Luis & Pastor, Jesús & Aparicio, Juan, 2010. "The Directional Profit Efficiency Measure: On Why Profit Inefficiency is either Technical or Allocative," Working Papers in Economic Theory 2010/09, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  3. Timo Kuosmanen & Timo Sipiläinen, 2009. "Exact decomposition of the Fisher ideal total factor productivity index," Journal of Productivity Analysis, Springer, vol. 31(3), pages 137-150, June.
  4. Massuanganhe, Israel Jacob, 2008. "Policies, Natural Resource Governance and Local Development," Ph.D Degree Theses 53061, University of the Free State, Department of Agricultural Economics.
  5. Laurens Cherchye & Timo Kuosmanen & Thierry Post, 2001. "FDH Directional Distance Functions with an Application to European Commercial Banks," Journal of Productivity Analysis, Springer, vol. 15(3), pages 201-215, January.
  6. Silva Portela, Maria Conceicao A. & Thanassoulis, Emmanuel, 2005. "Profitability of a sample of Portuguese bank branches and its decomposition into technical and allocative components," European Journal of Operational Research, Elsevier, vol. 162(3), pages 850-866, May.
  7. Walter Briec & Kristiaan Kerstens, 2008. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Working Papers 2008-ECO-11, IESEG School of Management.
  8. Zofío, José Luis & Prieto, Angel, 2005. "Return to Dollar, Generalized Distance Function and the Fisher Productivity Index," Working Papers in Economic Theory 2005/01, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  9. Subhash C. Ray, 2004. "The Directional Distance Function and Measurement of Super-Efficiency: An Application to Airlines Data," Working papers 2004-16, University of Connecticut, Department of Economics.
  10. Jiménez, Fernando & Zabala Iturriagagoitia, Jon Mikel & Zofío, José Luis, 2007. "Efficiency in Public Research Centers: Evaluating the Spanish Food Technology Program," Working Papers in Economic Theory 2007/04, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  11. Pablo Arocena & Ariadna Garc�a-Prado, 2007. "Accounting for quality in the measurement of hospital performance: evidence from Costa Rica," Health Economics, John Wiley & Sons, Ltd., vol. 16(7), pages 667-685.
  12. Elvira Silva & Alfons Oude Lansink, 2013. "Dynamic Efficiency Measurement: A Directional Distance Function Approach," CEF.UP Working Papers 1307, Universidade do Porto, Faculdade de Economia do Porto.
  13. Dalton, Timothy J., 2004. "Indivisible And Spatial Components Of Dairy Firm Efficiency," 2004 Annual meeting, August 1-4, Denver, CO 20320, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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